Properties

Label 7225.2.a.bg.1.4
Level 72257225
Weight 22
Character 7225.1
Self dual yes
Analytic conductor 57.69257.692
Analytic rank 00
Dimension 66
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7225,2,Mod(1,7225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7225, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7225.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 7225=52172 7225 = 5^{2} \cdot 17^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 7225.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 57.691915460457.6919154604
Analytic rank: 00
Dimension: 66
Coefficient field: 6.6.93924352.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x617x4+73x267 x^{6} - 17x^{4} + 73x^{2} - 67 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 425)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.4
Root 1.122611.12261 of defining polynomial
Character χ\chi == 7225.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+0.311108q2+1.12261q31.90321q4+0.349253q6+3.60843q71.21432q81.73975q95.74499q112.13656q12+2.59210q13+1.12261q14+3.42864q160.541249q184.28100q19+4.05086q211.78731q22+1.47186q231.36321q24+0.806424q265.32089q276.86760q28+5.50439q29+8.33946q31+3.49532q326.44938q33+3.31111q366.20290q371.33185q38+2.90992q39+3.95768q41+1.26025q429.76049q43+10.9339q44+0.457908q46+6.62222q47+3.84902q48+6.02074q494.93332q520.658781q531.65537q544.38178q564.80589q57+1.71246q585.95407q59+8.76357q61+2.59447q626.27775q635.76986q642.00645q660.428639q67+1.65233q69+1.36321q71+2.11261q723.25917q731.92977q74+8.14764q7620.7304q77+0.905299q78+1.89597q790.754037q81+1.23127q82+16.6637q837.70964q843.03657q86+6.17929q87+6.97626q883.52543q89+9.35342q912.80127q92+9.36196q93+2.06022q94+3.92388q96+11.7073q97+1.87310q98+9.99483q99+O(q100)q+0.311108 q^{2} +1.12261 q^{3} -1.90321 q^{4} +0.349253 q^{6} +3.60843 q^{7} -1.21432 q^{8} -1.73975 q^{9} -5.74499 q^{11} -2.13656 q^{12} +2.59210 q^{13} +1.12261 q^{14} +3.42864 q^{16} -0.541249 q^{18} -4.28100 q^{19} +4.05086 q^{21} -1.78731 q^{22} +1.47186 q^{23} -1.36321 q^{24} +0.806424 q^{26} -5.32089 q^{27} -6.86760 q^{28} +5.50439 q^{29} +8.33946 q^{31} +3.49532 q^{32} -6.44938 q^{33} +3.31111 q^{36} -6.20290 q^{37} -1.33185 q^{38} +2.90992 q^{39} +3.95768 q^{41} +1.26025 q^{42} -9.76049 q^{43} +10.9339 q^{44} +0.457908 q^{46} +6.62222 q^{47} +3.84902 q^{48} +6.02074 q^{49} -4.93332 q^{52} -0.658781 q^{53} -1.65537 q^{54} -4.38178 q^{56} -4.80589 q^{57} +1.71246 q^{58} -5.95407 q^{59} +8.76357 q^{61} +2.59447 q^{62} -6.27775 q^{63} -5.76986 q^{64} -2.00645 q^{66} -0.428639 q^{67} +1.65233 q^{69} +1.36321 q^{71} +2.11261 q^{72} -3.25917 q^{73} -1.92977 q^{74} +8.14764 q^{76} -20.7304 q^{77} +0.905299 q^{78} +1.89597 q^{79} -0.754037 q^{81} +1.23127 q^{82} +16.6637 q^{83} -7.70964 q^{84} -3.03657 q^{86} +6.17929 q^{87} +6.97626 q^{88} -3.52543 q^{89} +9.35342 q^{91} -2.80127 q^{92} +9.36196 q^{93} +2.06022 q^{94} +3.92388 q^{96} +11.7073 q^{97} +1.87310 q^{98} +9.99483 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q+2q2+2q4+6q8+16q9+2q136q1616q1812q192q2122q266q32+28q33+20q36+32q38+34q42+8q43+40q474q49+16q98+O(q100) 6 q + 2 q^{2} + 2 q^{4} + 6 q^{8} + 16 q^{9} + 2 q^{13} - 6 q^{16} - 16 q^{18} - 12 q^{19} - 2 q^{21} - 22 q^{26} - 6 q^{32} + 28 q^{33} + 20 q^{36} + 32 q^{38} + 34 q^{42} + 8 q^{43} + 40 q^{47} - 4 q^{49}+ \cdots - 16 q^{98}+O(q^{100}) Copy content Toggle raw display

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.311108 0.219986 0.109993 0.993932i 0.464917π-0.464917\pi
0.109993 + 0.993932i 0.464917π0.464917\pi
33 1.12261 0.648139 0.324070 0.946033i 0.394949π-0.394949\pi
0.324070 + 0.946033i 0.394949π0.394949\pi
44 −1.90321 −0.951606
55 0 0
66 0.349253 0.142582
77 3.60843 1.36386 0.681929 0.731419i 0.261141π-0.261141\pi
0.681929 + 0.731419i 0.261141π0.261141\pi
88 −1.21432 −0.429327
99 −1.73975 −0.579916
1010 0 0
1111 −5.74499 −1.73218 −0.866090 0.499888i 0.833374π-0.833374\pi
−0.866090 + 0.499888i 0.833374π0.833374\pi
1212 −2.13656 −0.616773
1313 2.59210 0.718920 0.359460 0.933160i 0.382961π-0.382961\pi
0.359460 + 0.933160i 0.382961π0.382961\pi
1414 1.12261 0.300030
1515 0 0
1616 3.42864 0.857160
1717 0 0
1818 −0.541249 −0.127574
1919 −4.28100 −0.982128 −0.491064 0.871124i 0.663392π-0.663392\pi
−0.491064 + 0.871124i 0.663392π0.663392\pi
2020 0 0
2121 4.05086 0.883969
2222 −1.78731 −0.381056
2323 1.47186 0.306905 0.153452 0.988156i 0.450961π-0.450961\pi
0.153452 + 0.988156i 0.450961π0.450961\pi
2424 −1.36321 −0.278264
2525 0 0
2626 0.806424 0.158153
2727 −5.32089 −1.02401
2828 −6.86760 −1.29785
2929 5.50439 1.02214 0.511070 0.859539i 0.329249π-0.329249\pi
0.511070 + 0.859539i 0.329249π0.329249\pi
3030 0 0
3131 8.33946 1.49781 0.748906 0.662676i 0.230579π-0.230579\pi
0.748906 + 0.662676i 0.230579π0.230579\pi
3232 3.49532 0.617890
3333 −6.44938 −1.12269
3434 0 0
3535 0 0
3636 3.31111 0.551851
3737 −6.20290 −1.01975 −0.509875 0.860248i 0.670308π-0.670308\pi
−0.509875 + 0.860248i 0.670308π0.670308\pi
3838 −1.33185 −0.216055
3939 2.90992 0.465960
4040 0 0
4141 3.95768 0.618086 0.309043 0.951048i 0.399991π-0.399991\pi
0.309043 + 0.951048i 0.399991π0.399991\pi
4242 1.26025 0.194461
4343 −9.76049 −1.48846 −0.744230 0.667923i 0.767184π-0.767184\pi
−0.744230 + 0.667923i 0.767184π0.767184\pi
4444 10.9339 1.64835
4545 0 0
4646 0.457908 0.0675148
4747 6.62222 0.965949 0.482975 0.875634i 0.339556π-0.339556\pi
0.482975 + 0.875634i 0.339556π0.339556\pi
4848 3.84902 0.555559
4949 6.02074 0.860106
5050 0 0
5151 0 0
5252 −4.93332 −0.684129
5353 −0.658781 −0.0904905 −0.0452452 0.998976i 0.514407π-0.514407\pi
−0.0452452 + 0.998976i 0.514407π0.514407\pi
5454 −1.65537 −0.225267
5555 0 0
5656 −4.38178 −0.585540
5757 −4.80589 −0.636555
5858 1.71246 0.224857
5959 −5.95407 −0.775154 −0.387577 0.921837i 0.626688π-0.626688\pi
−0.387577 + 0.921837i 0.626688π0.626688\pi
6060 0 0
6161 8.76357 1.12206 0.561030 0.827796i 0.310405π-0.310405\pi
0.561030 + 0.827796i 0.310405π0.310405\pi
6262 2.59447 0.329498
6363 −6.27775 −0.790922
6464 −5.76986 −0.721232
6565 0 0
6666 −2.00645 −0.246977
6767 −0.428639 −0.0523666 −0.0261833 0.999657i 0.508335π-0.508335\pi
−0.0261833 + 0.999657i 0.508335π0.508335\pi
6868 0 0
6969 1.65233 0.198917
7070 0 0
7171 1.36321 0.161783 0.0808915 0.996723i 0.474223π-0.474223\pi
0.0808915 + 0.996723i 0.474223π0.474223\pi
7272 2.11261 0.248973
7373 −3.25917 −0.381457 −0.190729 0.981643i 0.561085π-0.561085\pi
−0.190729 + 0.981643i 0.561085π0.561085\pi
7474 −1.92977 −0.224331
7575 0 0
7676 8.14764 0.934599
7777 −20.7304 −2.36245
7878 0.905299 0.102505
7979 1.89597 0.213313 0.106656 0.994296i 0.465985π-0.465985\pi
0.106656 + 0.994296i 0.465985π0.465985\pi
8080 0 0
8181 −0.754037 −0.0837819
8282 1.23127 0.135970
8383 16.6637 1.82908 0.914540 0.404497i 0.132553π-0.132553\pi
0.914540 + 0.404497i 0.132553π0.132553\pi
8484 −7.70964 −0.841190
8585 0 0
8686 −3.03657 −0.327441
8787 6.17929 0.662489
8888 6.97626 0.743671
8989 −3.52543 −0.373695 −0.186847 0.982389i 0.559827π-0.559827\pi
−0.186847 + 0.982389i 0.559827π0.559827\pi
9090 0 0
9191 9.35342 0.980505
9292 −2.80127 −0.292052
9393 9.36196 0.970790
9494 2.06022 0.212496
9595 0 0
9696 3.92388 0.400479
9797 11.7073 1.18870 0.594348 0.804208i 0.297410π-0.297410\pi
0.594348 + 0.804208i 0.297410π0.297410\pi
9898 1.87310 0.189212
9999 9.99483 1.00452
100100 0 0
101101 3.96989 0.395019 0.197509 0.980301i 0.436715π-0.436715\pi
0.197509 + 0.980301i 0.436715π0.436715\pi
102102 0 0
103103 −4.23506 −0.417293 −0.208647 0.977991i 0.566906π-0.566906\pi
−0.208647 + 0.977991i 0.566906π0.566906\pi
104104 −3.14764 −0.308652
105105 0 0
106106 −0.204952 −0.0199067
107107 11.8392 1.14454 0.572271 0.820065i 0.306063π-0.306063\pi
0.572271 + 0.820065i 0.306063π0.306063\pi
108108 10.1268 0.974449
109109 12.0227 1.15157 0.575785 0.817601i 0.304697π-0.304697\pi
0.575785 + 0.817601i 0.304697π0.304697\pi
110110 0 0
111111 −6.96343 −0.660940
112112 12.3720 1.16904
113113 10.7915 1.01518 0.507588 0.861600i 0.330537π-0.330537\pi
0.507588 + 0.861600i 0.330537π0.330537\pi
114114 −1.49515 −0.140034
115115 0 0
116116 −10.4760 −0.972675
117117 −4.50961 −0.416913
118118 −1.85236 −0.170523
119119 0 0
120120 0 0
121121 22.0049 2.00045
122122 2.72641 0.246838
123123 4.44293 0.400605
124124 −15.8718 −1.42533
125125 0 0
126126 −1.95306 −0.173992
127127 17.1383 1.52078 0.760388 0.649469i 0.225009π-0.225009\pi
0.760388 + 0.649469i 0.225009π0.225009\pi
128128 −8.78568 −0.776552
129129 −10.9572 −0.964730
130130 0 0
131131 8.89551 0.777204 0.388602 0.921406i 0.372958π-0.372958\pi
0.388602 + 0.921406i 0.372958π0.372958\pi
132132 12.2745 1.06836
133133 −15.4477 −1.33948
134134 −0.133353 −0.0115200
135135 0 0
136136 0 0
137137 −14.0716 −1.20222 −0.601109 0.799167i 0.705274π-0.705274\pi
−0.601109 + 0.799167i 0.705274π0.705274\pi
138138 0.514052 0.0437590
139139 −16.7876 −1.42390 −0.711952 0.702228i 0.752189π-0.752189\pi
−0.711952 + 0.702228i 0.752189π0.752189\pi
140140 0 0
141141 7.43416 0.626070
142142 0.424104 0.0355901
143143 −14.8916 −1.24530
144144 −5.96497 −0.497081
145145 0 0
146146 −1.01395 −0.0839155
147147 6.75895 0.557468
148148 11.8054 0.970400
149149 −4.76494 −0.390359 −0.195179 0.980768i 0.562529π-0.562529\pi
−0.195179 + 0.980768i 0.562529π0.562529\pi
150150 0 0
151151 −2.99063 −0.243374 −0.121687 0.992569i 0.538830π-0.538830\pi
−0.121687 + 0.992569i 0.538830π0.538830\pi
152152 5.19850 0.421654
153153 0 0
154154 −6.44938 −0.519706
155155 0 0
156156 −5.53820 −0.443411
157157 13.9447 1.11291 0.556454 0.830878i 0.312162π-0.312162\pi
0.556454 + 0.830878i 0.312162π0.312162\pi
158158 0.589850 0.0469260
159159 −0.739554 −0.0586504
160160 0 0
161161 5.31111 0.418574
162162 −0.234587 −0.0184309
163163 −8.65491 −0.677905 −0.338953 0.940803i 0.610073π-0.610073\pi
−0.338953 + 0.940803i 0.610073π0.610073\pi
164164 −7.53230 −0.588174
165165 0 0
166166 5.18421 0.402373
167167 0.773357 0.0598442 0.0299221 0.999552i 0.490474π-0.490474\pi
0.0299221 + 0.999552i 0.490474π0.490474\pi
168168 −4.91903 −0.379512
169169 −6.28100 −0.483154
170170 0 0
171171 7.44785 0.569551
172172 18.5763 1.41643
173173 −2.41097 −0.183302 −0.0916511 0.995791i 0.529214π-0.529214\pi
−0.0916511 + 0.995791i 0.529214π0.529214\pi
174174 1.92242 0.145739
175175 0 0
176176 −19.6975 −1.48476
177177 −6.68409 −0.502407
178178 −1.09679 −0.0822077
179179 18.4558 1.37945 0.689727 0.724070i 0.257731π-0.257731\pi
0.689727 + 0.724070i 0.257731π0.257731\pi
180180 0 0
181181 20.6366 1.53391 0.766953 0.641703i 0.221772π-0.221772\pi
0.766953 + 0.641703i 0.221772π0.221772\pi
182182 2.90992 0.215698
183183 9.83807 0.727251
184184 −1.78731 −0.131762
185185 0 0
186186 2.91258 0.213561
187187 0 0
188188 −12.6035 −0.919203
189189 −19.2000 −1.39660
190190 0 0
191191 22.8113 1.65057 0.825286 0.564716i 0.191014π-0.191014\pi
0.825286 + 0.564716i 0.191014π0.191014\pi
192192 −6.47730 −0.467459
193193 −19.7208 −1.41953 −0.709767 0.704437i 0.751200π-0.751200\pi
−0.709767 + 0.704437i 0.751200π0.751200\pi
194194 3.64223 0.261497
195195 0 0
196196 −11.4588 −0.818482
197197 12.8870 0.918160 0.459080 0.888395i 0.348179π-0.348179\pi
0.459080 + 0.888395i 0.348179π0.348179\pi
198198 3.10947 0.220980
199199 6.44350 0.456767 0.228384 0.973571i 0.426656π-0.426656\pi
0.228384 + 0.973571i 0.426656π0.426656\pi
200200 0 0
201201 −0.481195 −0.0339409
202202 1.23506 0.0868988
203203 19.8622 1.39405
204204 0 0
205205 0 0
206206 −1.31756 −0.0917988
207207 −2.56067 −0.177979
208208 8.88739 0.616230
209209 24.5943 1.70122
210210 0 0
211211 −11.3580 −0.781920 −0.390960 0.920408i 0.627857π-0.627857\pi
−0.390960 + 0.920408i 0.627857π0.627857\pi
212212 1.25380 0.0861113
213213 1.53035 0.104858
214214 3.68328 0.251784
215215 0 0
216216 6.46126 0.439633
217217 30.0923 2.04280
218218 3.74037 0.253330
219219 −3.65878 −0.247237
220220 0 0
221221 0 0
222222 −2.16638 −0.145398
223223 0.888922 0.0595266 0.0297633 0.999557i 0.490525π-0.490525\pi
0.0297633 + 0.999557i 0.490525π0.490525\pi
224224 12.6126 0.842714
225225 0 0
226226 3.35731 0.223325
227227 12.9280 0.858064 0.429032 0.903289i 0.358855π-0.358855\pi
0.429032 + 0.903289i 0.358855π0.358855\pi
228228 9.14662 0.605750
229229 −2.83161 −0.187118 −0.0935591 0.995614i 0.529824π-0.529824\pi
−0.0935591 + 0.995614i 0.529824π0.529824\pi
230230 0 0
231231 −23.2721 −1.53119
232232 −6.68409 −0.438832
233233 −19.9381 −1.30619 −0.653094 0.757277i 0.726529π-0.726529\pi
−0.653094 + 0.757277i 0.726529π0.726529\pi
234234 −1.40297 −0.0917153
235235 0 0
236236 11.3319 0.737641
237237 2.12843 0.138256
238238 0 0
239239 27.2859 1.76498 0.882490 0.470332i 0.155866π-0.155866\pi
0.882490 + 0.470332i 0.155866π0.155866\pi
240240 0 0
241241 −3.57462 −0.230262 −0.115131 0.993350i 0.536729π-0.536729\pi
−0.115131 + 0.993350i 0.536729π0.536729\pi
242242 6.84590 0.440071
243243 15.1162 0.969703
244244 −16.6789 −1.06776
245245 0 0
246246 1.38223 0.0881278
247247 −11.0968 −0.706072
248248 −10.1268 −0.643051
249249 18.7068 1.18550
250250 0 0
251251 17.6128 1.11171 0.555857 0.831278i 0.312390π-0.312390\pi
0.555857 + 0.831278i 0.312390π0.312390\pi
252252 11.9479 0.752646
253253 −8.45584 −0.531614
254254 5.33185 0.334550
255255 0 0
256256 8.80642 0.550401
257257 20.5462 1.28163 0.640817 0.767693i 0.278596π-0.278596\pi
0.640817 + 0.767693i 0.278596π0.278596\pi
258258 −3.40888 −0.212227
259259 −22.3827 −1.39079
260260 0 0
261261 −9.57625 −0.592755
262262 2.76746 0.170974
263263 8.38715 0.517174 0.258587 0.965988i 0.416743π-0.416743\pi
0.258587 + 0.965988i 0.416743π0.416743\pi
264264 7.83161 0.482002
265265 0 0
266266 −4.80589 −0.294668
267267 −3.95768 −0.242206
268268 0.815792 0.0498324
269269 −12.4058 −0.756395 −0.378197 0.925725i 0.623456π-0.623456\pi
−0.378197 + 0.925725i 0.623456π0.623456\pi
270270 0 0
271271 −7.13828 −0.433619 −0.216810 0.976214i 0.569565π-0.569565\pi
−0.216810 + 0.976214i 0.569565π0.569565\pi
272272 0 0
273273 10.5002 0.635503
274274 −4.37778 −0.264472
275275 0 0
276276 −3.14473 −0.189290
277277 −20.4193 −1.22688 −0.613438 0.789743i 0.710214π-0.710214\pi
−0.613438 + 0.789743i 0.710214π0.710214\pi
278278 −5.22275 −0.313240
279279 −14.5086 −0.868605
280280 0 0
281281 −29.1432 −1.73854 −0.869269 0.494340i 0.835410π-0.835410\pi
−0.869269 + 0.494340i 0.835410π0.835410\pi
282282 2.31283 0.137727
283283 −9.16991 −0.545095 −0.272547 0.962142i 0.587866π-0.587866\pi
−0.272547 + 0.962142i 0.587866π0.587866\pi
284284 −2.59447 −0.153954
285285 0 0
286286 −4.63290 −0.273949
287287 14.2810 0.842981
288288 −6.08097 −0.358324
289289 0 0
290290 0 0
291291 13.1427 0.770440
292292 6.20290 0.362997
293293 16.2351 0.948463 0.474231 0.880400i 0.342726π-0.342726\pi
0.474231 + 0.880400i 0.342726π0.342726\pi
294294 2.10276 0.122636
295295 0 0
296296 7.53230 0.437806
297297 30.5684 1.77376
298298 −1.48241 −0.0858737
299299 3.81522 0.220640
300300 0 0
301301 −35.2200 −2.03005
302302 −0.930409 −0.0535390
303303 4.45664 0.256027
304304 −14.6780 −0.841841
305305 0 0
306306 0 0
307307 −3.37778 −0.192780 −0.0963902 0.995344i 0.530730π-0.530730\pi
−0.0963902 + 0.995344i 0.530730π0.530730\pi
308308 39.4543 2.24812
309309 −4.75432 −0.270464
310310 0 0
311311 7.95641 0.451166 0.225583 0.974224i 0.427571π-0.427571\pi
0.225583 + 0.974224i 0.427571π0.427571\pi
312312 −3.53358 −0.200049
313313 6.83380 0.386269 0.193135 0.981172i 0.438135π-0.438135\pi
0.193135 + 0.981172i 0.438135π0.438135\pi
314314 4.33830 0.244825
315315 0 0
316316 −3.60843 −0.202990
317317 −27.1550 −1.52517 −0.762587 0.646886i 0.776071π-0.776071\pi
−0.762587 + 0.646886i 0.776071π0.776071\pi
318318 −0.230081 −0.0129023
319319 −31.6227 −1.77053
320320 0 0
321321 13.2908 0.741822
322322 1.65233 0.0920806
323323 0 0
324324 1.43509 0.0797274
325325 0 0
326326 −2.69261 −0.149130
327327 13.4968 0.746377
328328 −4.80589 −0.265361
329329 23.8958 1.31742
330330 0 0
331331 20.3783 1.12009 0.560045 0.828462i 0.310784π-0.310784\pi
0.560045 + 0.828462i 0.310784π0.310784\pi
332332 −31.7146 −1.74056
333333 10.7915 0.591369
334334 0.240597 0.0131649
335335 0 0
336336 13.8889 0.757703
337337 −4.70775 −0.256447 −0.128224 0.991745i 0.540928π-0.540928\pi
−0.128224 + 0.991745i 0.540928π0.540928\pi
338338 −1.95407 −0.106287
339339 12.1146 0.657976
340340 0 0
341341 −47.9101 −2.59448
342342 2.31708 0.125294
343343 −3.53358 −0.190795
344344 11.8524 0.639036
345345 0 0
346346 −0.750070 −0.0403240
347347 35.3520 1.89779 0.948896 0.315588i 0.102202π-0.102202\pi
0.948896 + 0.315588i 0.102202π0.102202\pi
348348 −11.7605 −0.630428
349349 25.0558 1.34121 0.670603 0.741817i 0.266036π-0.266036\pi
0.670603 + 0.741817i 0.266036π0.266036\pi
350350 0 0
351351 −13.7923 −0.736178
352352 −20.0806 −1.07030
353353 −13.6953 −0.728930 −0.364465 0.931217i 0.618748π-0.618748\pi
−0.364465 + 0.931217i 0.618748π0.618748\pi
354354 −2.07947 −0.110523
355355 0 0
356356 6.70964 0.355610
357357 0 0
358358 5.74176 0.303461
359359 −2.53480 −0.133781 −0.0668907 0.997760i 0.521308π-0.521308\pi
−0.0668907 + 0.997760i 0.521308π0.521308\pi
360360 0 0
361361 −0.673071 −0.0354248
362362 6.42021 0.337439
363363 24.7029 1.29657
364364 −17.8015 −0.933054
365365 0 0
366366 3.06070 0.159985
367367 −36.3426 −1.89707 −0.948535 0.316673i 0.897434π-0.897434\pi
−0.948535 + 0.316673i 0.897434π0.897434\pi
368368 5.04649 0.263066
369369 −6.88536 −0.358438
370370 0 0
371371 −2.37716 −0.123416
372372 −17.8178 −0.923810
373373 12.7714 0.661278 0.330639 0.943757i 0.392736π-0.392736\pi
0.330639 + 0.943757i 0.392736π0.392736\pi
374374 0 0
375375 0 0
376376 −8.04149 −0.414708
377377 14.2680 0.734837
378378 −5.97328 −0.307232
379379 −22.1495 −1.13774 −0.568872 0.822426i 0.692620π-0.692620\pi
−0.568872 + 0.822426i 0.692620π0.692620\pi
380380 0 0
381381 19.2396 0.985674
382382 7.09679 0.363103
383383 −1.95407 −0.0998482 −0.0499241 0.998753i 0.515898π-0.515898\pi
−0.0499241 + 0.998753i 0.515898π0.515898\pi
384384 −9.86289 −0.503314
385385 0 0
386386 −6.13529 −0.312278
387387 16.9808 0.863182
388388 −22.2815 −1.13117
389389 7.91258 0.401184 0.200592 0.979675i 0.435713π-0.435713\pi
0.200592 + 0.979675i 0.435713π0.435713\pi
390390 0 0
391391 0 0
392392 −7.31111 −0.369267
393393 9.98619 0.503736
394394 4.00924 0.201983
395395 0 0
396396 −19.0223 −0.955906
397397 −9.24476 −0.463981 −0.231991 0.972718i 0.574524π-0.574524\pi
−0.231991 + 0.972718i 0.574524π0.574524\pi
398398 2.00462 0.100483
399399 −17.3417 −0.868171
400400 0 0
401401 21.4848 1.07290 0.536450 0.843932i 0.319765π-0.319765\pi
0.536450 + 0.843932i 0.319765π0.319765\pi
402402 −0.149703 −0.00746653
403403 21.6168 1.07681
404404 −7.55554 −0.375902
405405 0 0
406406 6.17929 0.306673
407407 35.6356 1.76639
408408 0 0
409409 18.1669 0.898293 0.449147 0.893458i 0.351728π-0.351728\pi
0.449147 + 0.893458i 0.351728π0.351728\pi
410410 0 0
411411 −15.7969 −0.779204
412412 8.06022 0.397099
413413 −21.4848 −1.05720
414414 −0.796644 −0.0391529
415415 0 0
416416 9.06022 0.444214
417417 −18.8459 −0.922888
418418 7.65147 0.374246
419419 −14.3589 −0.701476 −0.350738 0.936474i 0.614069π-0.614069\pi
−0.350738 + 0.936474i 0.614069π0.614069\pi
420420 0 0
421421 3.96989 0.193481 0.0967403 0.995310i 0.469158π-0.469158\pi
0.0967403 + 0.995310i 0.469158π0.469158\pi
422422 −3.53358 −0.172012
423423 −11.5210 −0.560169
424424 0.799970 0.0388500
425425 0 0
426426 0.476104 0.0230673
427427 31.6227 1.53033
428428 −22.5326 −1.08915
429429 −16.7175 −0.807127
430430 0 0
431431 32.9337 1.58636 0.793181 0.608985i 0.208423π-0.208423\pi
0.793181 + 0.608985i 0.208423π0.208423\pi
432432 −18.2434 −0.877736
433433 38.2306 1.83725 0.918623 0.395135i 0.129302π-0.129302\pi
0.918623 + 0.395135i 0.129302π0.129302\pi
434434 9.36196 0.449389
435435 0 0
436436 −22.8818 −1.09584
437437 −6.30104 −0.301420
438438 −1.13828 −0.0543889
439439 −0.664702 −0.0317245 −0.0158622 0.999874i 0.505049π-0.505049\pi
−0.0158622 + 0.999874i 0.505049π0.505049\pi
440440 0 0
441441 −10.4746 −0.498789
442442 0 0
443443 27.5669 1.30974 0.654872 0.755740i 0.272723π-0.272723\pi
0.654872 + 0.755740i 0.272723π0.272723\pi
444444 13.2529 0.628954
445445 0 0
446446 0.276551 0.0130950
447447 −5.34916 −0.253007
448448 −20.8201 −0.983658
449449 17.4756 0.824723 0.412362 0.911020i 0.364704π-0.364704\pi
0.412362 + 0.911020i 0.364704π0.364704\pi
450450 0 0
451451 −22.7368 −1.07064
452452 −20.5385 −0.966048
453453 −3.35731 −0.157740
454454 4.02201 0.188762
455455 0 0
456456 5.83589 0.273290
457457 −13.0350 −0.609753 −0.304877 0.952392i 0.598615π-0.598615\pi
−0.304877 + 0.952392i 0.598615π0.598615\pi
458458 −0.880937 −0.0411635
459459 0 0
460460 0 0
461461 10.9491 0.509953 0.254976 0.966947i 0.417932π-0.417932\pi
0.254976 + 0.966947i 0.417932π0.417932\pi
462462 −7.24014 −0.336842
463463 −17.2400 −0.801210 −0.400605 0.916251i 0.631200π-0.631200\pi
−0.400605 + 0.916251i 0.631200π0.631200\pi
464464 18.8726 0.876138
465465 0 0
466466 −6.20290 −0.287344
467467 −0.0414872 −0.00191980 −0.000959899 1.00000i 0.500306π-0.500306\pi
−0.000959899 1.00000i 0.500306π0.500306\pi
468468 8.58274 0.396737
469469 −1.54671 −0.0714206
470470 0 0
471471 15.6545 0.721319
472472 7.23014 0.332794
473473 56.0739 2.57828
474474 0.662171 0.0304145
475475 0 0
476476 0 0
477477 1.14611 0.0524769
478478 8.48886 0.388272
479479 35.4606 1.62024 0.810118 0.586266i 0.199403π-0.199403\pi
0.810118 + 0.586266i 0.199403π0.199403\pi
480480 0 0
481481 −16.0786 −0.733119
482482 −1.11209 −0.0506545
483483 5.96230 0.271294
484484 −41.8800 −1.90364
485485 0 0
486486 4.70276 0.213321
487487 24.6691 1.11787 0.558933 0.829213i 0.311211π-0.311211\pi
0.558933 + 0.829213i 0.311211π0.311211\pi
488488 −10.6418 −0.481730
489489 −9.71609 −0.439377
490490 0 0
491491 −8.58073 −0.387243 −0.193621 0.981076i 0.562023π-0.562023\pi
−0.193621 + 0.981076i 0.562023π0.562023\pi
492492 −8.45584 −0.381219
493493 0 0
494494 −3.45230 −0.155326
495495 0 0
496496 28.5930 1.28386
497497 4.91903 0.220649
498498 5.81984 0.260793
499499 8.48917 0.380027 0.190014 0.981781i 0.439147π-0.439147\pi
0.190014 + 0.981781i 0.439147π0.439147\pi
500500 0 0
501501 0.868178 0.0387873
502502 5.47949 0.244562
503503 24.1879 1.07849 0.539244 0.842150i 0.318710π-0.318710\pi
0.539244 + 0.842150i 0.318710π0.318710\pi
504504 7.62320 0.339564
505505 0 0
506506 −2.63068 −0.116948
507507 −7.05111 −0.313151
508508 −32.6178 −1.44718
509509 −25.8671 −1.14654 −0.573270 0.819366i 0.694325π-0.694325\pi
−0.573270 + 0.819366i 0.694325π0.694325\pi
510510 0 0
511511 −11.7605 −0.520253
512512 20.3111 0.897633
513513 22.7787 1.00570
514514 6.39207 0.281942
515515 0 0
516516 20.8539 0.918042
517517 −38.0446 −1.67320
518518 −6.96343 −0.305956
519519 −2.70657 −0.118805
520520 0 0
521521 11.4900 0.503385 0.251693 0.967807i 0.419013π-0.419013\pi
0.251693 + 0.967807i 0.419013π0.419013\pi
522522 −2.97925 −0.130398
523523 33.0509 1.44521 0.722606 0.691260i 0.242944π-0.242944\pi
0.722606 + 0.691260i 0.242944π0.242944\pi
524524 −16.9300 −0.739592
525525 0 0
526526 2.60931 0.113771
527527 0 0
528528 −22.1126 −0.962328
529529 −20.8336 −0.905810
530530 0 0
531531 10.3586 0.449524
532532 29.4002 1.27466
533533 10.2587 0.444354
534534 −1.23127 −0.0532820
535535 0 0
536536 0.520505 0.0224824
537537 20.7187 0.894078
538538 −3.85954 −0.166397
539539 −34.5891 −1.48986
540540 0 0
541541 19.7884 0.850770 0.425385 0.905013i 0.360139π-0.360139\pi
0.425385 + 0.905013i 0.360139π0.360139\pi
542542 −2.22077 −0.0953904
543543 23.1669 0.994185
544544 0 0
545545 0 0
546546 3.26671 0.139802
547547 −15.4815 −0.661940 −0.330970 0.943641i 0.607376π-0.607376\pi
−0.330970 + 0.943641i 0.607376π0.607376\pi
548548 26.7812 1.14404
549549 −15.2464 −0.650700
550550 0 0
551551 −23.5643 −1.00387
552552 −2.00645 −0.0854003
553553 6.84146 0.290928
554554 −6.35260 −0.269896
555555 0 0
556556 31.9503 1.35500
557557 −15.3477 −0.650302 −0.325151 0.945662i 0.605415π-0.605415\pi
−0.325151 + 0.945662i 0.605415π0.605415\pi
558558 −4.51373 −0.191081
559559 −25.3002 −1.07008
560560 0 0
561561 0 0
562562 −9.06668 −0.382455
563563 −14.3827 −0.606159 −0.303079 0.952965i 0.598015π-0.598015\pi
−0.303079 + 0.952965i 0.598015π0.598015\pi
564564 −14.1488 −0.595772
565565 0 0
566566 −2.85283 −0.119913
567567 −2.72089 −0.114267
568568 −1.65537 −0.0694578
569569 12.1432 0.509069 0.254535 0.967064i 0.418078π-0.418078\pi
0.254535 + 0.967064i 0.418078π0.418078\pi
570570 0 0
571571 2.88663 0.120802 0.0604009 0.998174i 0.480762π-0.480762\pi
0.0604009 + 0.998174i 0.480762π0.480762\pi
572572 28.3419 1.18503
573573 25.6082 1.06980
574574 4.44293 0.185444
575575 0 0
576576 10.0381 0.418254
577577 −3.10970 −0.129458 −0.0647291 0.997903i 0.520618π-0.520618\pi
−0.0647291 + 0.997903i 0.520618π0.520618\pi
578578 0 0
579579 −22.1388 −0.920055
580580 0 0
581581 60.1298 2.49460
582582 4.08880 0.169486
583583 3.78469 0.156746
584584 3.95768 0.163770
585585 0 0
586586 5.05086 0.208649
587587 −10.2034 −0.421140 −0.210570 0.977579i 0.567532π-0.567532\pi
−0.210570 + 0.977579i 0.567532π0.567532\pi
588588 −12.8637 −0.530490
589589 −35.7012 −1.47104
590590 0 0
591591 14.4671 0.595095
592592 −21.2675 −0.874089
593593 16.2301 0.666492 0.333246 0.942840i 0.391856π-0.391856\pi
0.333246 + 0.942840i 0.391856π0.391856\pi
594594 9.51008 0.390203
595595 0 0
596596 9.06868 0.371468
597597 7.23353 0.296049
598598 1.18694 0.0485378
599599 −8.43309 −0.344567 −0.172283 0.985047i 0.555114π-0.555114\pi
−0.172283 + 0.985047i 0.555114π0.555114\pi
600600 0 0
601601 −20.2535 −0.826160 −0.413080 0.910695i 0.635547π-0.635547\pi
−0.413080 + 0.910695i 0.635547π0.635547\pi
602602 −10.9572 −0.446583
603603 0.745724 0.0303682
604604 5.69181 0.231596
605605 0 0
606606 1.38649 0.0563225
607607 22.7732 0.924334 0.462167 0.886793i 0.347072π-0.347072\pi
0.462167 + 0.886793i 0.347072π0.347072\pi
608608 −14.9634 −0.606847
609609 22.2975 0.903540
610610 0 0
611611 17.1655 0.694441
612612 0 0
613613 −8.40636 −0.339530 −0.169765 0.985485i 0.554301π-0.554301\pi
−0.169765 + 0.985485i 0.554301π0.554301\pi
614614 −1.05086 −0.0424091
615615 0 0
616616 25.1733 1.01426
617617 14.8168 0.596500 0.298250 0.954488i 0.403597π-0.403597\pi
0.298250 + 0.954488i 0.403597π0.403597\pi
618618 −1.47911 −0.0594984
619619 −31.6221 −1.27100 −0.635500 0.772101i 0.719206π-0.719206\pi
−0.635500 + 0.772101i 0.719206π0.719206\pi
620620 0 0
621621 −7.83161 −0.314272
622622 2.47530 0.0992505
623623 −12.7212 −0.509666
624624 9.97707 0.399403
625625 0 0
626626 2.12605 0.0849740
627627 27.6098 1.10263
628628 −26.5397 −1.05905
629629 0 0
630630 0 0
631631 17.3733 0.691622 0.345811 0.938304i 0.387604π-0.387604\pi
0.345811 + 0.938304i 0.387604π0.387604\pi
632632 −2.30231 −0.0915810
633633 −12.7506 −0.506793
634634 −8.44812 −0.335518
635635 0 0
636636 1.40753 0.0558121
637637 15.6064 0.618348
638638 −9.83807 −0.389493
639639 −2.37164 −0.0938205
640640 0 0
641641 −7.26842 −0.287085 −0.143543 0.989644i 0.545849π-0.545849\pi
−0.143543 + 0.989644i 0.545849π0.545849\pi
642642 4.13488 0.163191
643643 4.40507 0.173719 0.0868595 0.996221i 0.472317π-0.472317\pi
0.0868595 + 0.996221i 0.472317π0.472317\pi
644644 −10.1082 −0.398317
645645 0 0
646646 0 0
647647 0.198022 0.00778504 0.00389252 0.999992i 0.498761π-0.498761\pi
0.00389252 + 0.999992i 0.498761π0.498761\pi
648648 0.915643 0.0359698
649649 34.2061 1.34271
650650 0 0
651651 33.7820 1.32402
652652 16.4721 0.645098
653653 −9.92723 −0.388482 −0.194241 0.980954i 0.562224π-0.562224\pi
−0.194241 + 0.980954i 0.562224π0.562224\pi
654654 4.19897 0.164193
655655 0 0
656656 13.5695 0.529798
657657 5.67014 0.221213
658658 7.43416 0.289814
659659 3.00492 0.117055 0.0585276 0.998286i 0.481359π-0.481359\pi
0.0585276 + 0.998286i 0.481359π0.481359\pi
660660 0 0
661661 −23.6923 −0.921523 −0.460762 0.887524i 0.652424π-0.652424\pi
−0.460762 + 0.887524i 0.652424π0.652424\pi
662662 6.33984 0.246405
663663 0 0
664664 −20.2351 −0.785273
665665 0 0
666666 3.35731 0.130093
667667 8.10171 0.313699
668668 −1.47186 −0.0569481
669669 0.997912 0.0385815
670670 0 0
671671 −50.3466 −1.94361
672672 14.1590 0.546196
673673 30.1968 1.16400 0.582001 0.813188i 0.302270π-0.302270\pi
0.582001 + 0.813188i 0.302270π0.302270\pi
674674 −1.46462 −0.0564150
675675 0 0
676676 11.9541 0.459772
677677 −47.9413 −1.84253 −0.921266 0.388933i 0.872844π-0.872844\pi
−0.921266 + 0.388933i 0.872844π0.872844\pi
678678 3.76895 0.144746
679679 42.2449 1.62121
680680 0 0
681681 14.5131 0.556145
682682 −14.9052 −0.570750
683683 1.41477 0.0541347 0.0270674 0.999634i 0.491383π-0.491383\pi
0.0270674 + 0.999634i 0.491383π0.491383\pi
684684 −14.1748 −0.541989
685685 0 0
686686 −1.09932 −0.0419723
687687 −3.17880 −0.121279
688688 −33.4652 −1.27585
689689 −1.70763 −0.0650554
690690 0 0
691691 1.36321 0.0518588 0.0259294 0.999664i 0.491745π-0.491745\pi
0.0259294 + 0.999664i 0.491745π0.491745\pi
692692 4.58858 0.174432
693693 36.0656 1.37002
694694 10.9983 0.417489
695695 0 0
696696 −7.50363 −0.284424
697697 0 0
698698 7.79505 0.295047
699699 −22.3827 −0.846592
700700 0 0
701701 −40.1990 −1.51829 −0.759147 0.650919i 0.774384π-0.774384\pi
−0.759147 + 0.650919i 0.774384π0.774384\pi
702702 −4.29089 −0.161949
703703 26.5546 1.00153
704704 33.1478 1.24930
705705 0 0
706706 −4.26073 −0.160355
707707 14.3251 0.538749
708708 12.7212 0.478094
709709 −19.4729 −0.731322 −0.365661 0.930748i 0.619157π-0.619157\pi
−0.365661 + 0.930748i 0.619157π0.619157\pi
710710 0 0
711711 −3.29850 −0.123704
712712 4.28100 0.160437
713713 12.2745 0.459685
714714 0 0
715715 0 0
716716 −35.1254 −1.31270
717717 30.6314 1.14395
718718 −0.788595 −0.0294301
719719 −21.9765 −0.819586 −0.409793 0.912179i 0.634399π-0.634399\pi
−0.409793 + 0.912179i 0.634399π0.634399\pi
720720 0 0
721721 −15.2819 −0.569128
722722 −0.209398 −0.00779297
723723 −4.01291 −0.149242
724724 −39.2758 −1.45967
725725 0 0
726726 7.68528 0.285227
727727 36.7007 1.36116 0.680578 0.732676i 0.261729π-0.261729\pi
0.680578 + 0.732676i 0.261729π0.261729\pi
728728 −11.3580 −0.420957
729729 19.2317 0.712284
730730 0 0
731731 0 0
732732 −18.7239 −0.692056
733733 −24.8666 −0.918471 −0.459235 0.888315i 0.651877π-0.651877\pi
−0.459235 + 0.888315i 0.651877π0.651877\pi
734734 −11.3065 −0.417330
735735 0 0
736736 5.14462 0.189633
737737 2.46253 0.0907085
738738 −2.14209 −0.0788514
739739 32.7368 1.20424 0.602122 0.798404i 0.294322π-0.294322\pi
0.602122 + 0.798404i 0.294322π0.294322\pi
740740 0 0
741741 −12.4574 −0.457633
742742 −0.739554 −0.0271499
743743 21.3762 0.784215 0.392108 0.919919i 0.371746π-0.371746\pi
0.392108 + 0.919919i 0.371746π0.371746\pi
744744 −11.3684 −0.416786
745745 0 0
746746 3.97328 0.145472
747747 −28.9906 −1.06071
748748 0 0
749749 42.7210 1.56099
750750 0 0
751751 −44.5557 −1.62586 −0.812930 0.582362i 0.802129π-0.802129\pi
−0.812930 + 0.582362i 0.802129π0.802129\pi
752752 22.7052 0.827973
753753 19.7724 0.720545
754754 4.43887 0.161654
755755 0 0
756756 36.5417 1.32901
757757 −12.1793 −0.442664 −0.221332 0.975199i 0.571040π-0.571040\pi
−0.221332 + 0.975199i 0.571040π0.571040\pi
758758 −6.89089 −0.250288
759759 −9.49260 −0.344560
760760 0 0
761761 7.18712 0.260533 0.130266 0.991479i 0.458417π-0.458417\pi
0.130266 + 0.991479i 0.458417π0.458417\pi
762762 5.98559 0.216835
763763 43.3832 1.57058
764764 −43.4148 −1.57069
765765 0 0
766766 −0.607926 −0.0219652
767767 −15.4336 −0.557274
768768 9.88618 0.356737
769769 14.9748 0.540005 0.270003 0.962860i 0.412975π-0.412975\pi
0.270003 + 0.962860i 0.412975π0.412975\pi
770770 0 0
771771 23.0653 0.830678
772772 37.5328 1.35084
773773 26.2938 0.945721 0.472860 0.881137i 0.343222π-0.343222\pi
0.472860 + 0.881137i 0.343222π0.343222\pi
774774 5.28286 0.189888
775775 0 0
776776 −14.2164 −0.510339
777777 −25.1270 −0.901428
778778 2.46167 0.0882550
779779 −16.9428 −0.607039
780780 0 0
781781 −7.83161 −0.280237
782782 0 0
783783 −29.2883 −1.04668
784784 20.6430 0.737249
785785 0 0
786786 3.10678 0.110815
787787 −9.35342 −0.333413 −0.166707 0.986007i 0.553313π-0.553313\pi
−0.166707 + 0.986007i 0.553313π0.553313\pi
788788 −24.5267 −0.873727
789789 9.41550 0.335201
790790 0 0
791791 38.9403 1.38456
792792 −12.1369 −0.431267
793793 22.7161 0.806672
794794 −2.87612 −0.102070
795795 0 0
796796 −12.2633 −0.434663
797797 29.4800 1.04423 0.522117 0.852874i 0.325142π-0.325142\pi
0.522117 + 0.852874i 0.325142π0.325142\pi
798798 −5.39514 −0.190986
799799 0 0
800800 0 0
801801 6.13335 0.216711
802802 6.68409 0.236024
803803 18.7239 0.660753
804804 0.915816 0.0322983
805805 0 0
806806 6.72514 0.236883
807807 −13.9269 −0.490249
808808 −4.82071 −0.169592
809809 35.1219 1.23482 0.617410 0.786642i 0.288182π-0.288182\pi
0.617410 + 0.786642i 0.288182π0.288182\pi
810810 0 0
811811 −17.5682 −0.616902 −0.308451 0.951240i 0.599811π-0.599811\pi
−0.308451 + 0.951240i 0.599811π0.599811\pi
812812 −37.8020 −1.32659
813813 −8.01350 −0.281046
814814 11.0865 0.388582
815815 0 0
816816 0 0
817817 41.7846 1.46186
818818 5.65185 0.197612
819819 −16.2726 −0.568610
820820 0 0
821821 −13.1043 −0.457343 −0.228672 0.973504i 0.573438π-0.573438\pi
−0.228672 + 0.973504i 0.573438π0.573438\pi
822822 −4.91454 −0.171414
823823 23.7638 0.828355 0.414178 0.910196i 0.364069π-0.364069\pi
0.414178 + 0.910196i 0.364069π0.364069\pi
824824 5.14272 0.179155
825825 0 0
826826 −6.68409 −0.232569
827827 −28.9423 −1.00642 −0.503211 0.864164i 0.667848π-0.667848\pi
−0.503211 + 0.864164i 0.667848π0.667848\pi
828828 4.87350 0.169366
829829 48.3131 1.67798 0.838992 0.544144i 0.183145π-0.183145\pi
0.838992 + 0.544144i 0.183145π0.183145\pi
830830 0 0
831831 −22.9229 −0.795187
832832 −14.9561 −0.518509
833833 0 0
834834 −5.86311 −0.203023
835835 0 0
836836 −46.8081 −1.61889
837837 −44.3733 −1.53377
838838 −4.46715 −0.154315
839839 −36.8238 −1.27130 −0.635650 0.771978i 0.719268π-0.719268\pi
−0.635650 + 0.771978i 0.719268π0.719268\pi
840840 0 0
841841 1.29835 0.0447707
842842 1.23506 0.0425631
843843 −32.7164 −1.12681
844844 21.6168 0.744079
845845 0 0
846846 −3.58427 −0.123230
847847 79.4031 2.72832
848848 −2.25872 −0.0775648
849849 −10.2942 −0.353297
850850 0 0
851851 −9.12981 −0.312966
852852 −2.91258 −0.0997833
853853 −29.8138 −1.02080 −0.510402 0.859936i 0.670503π-0.670503\pi
−0.510402 + 0.859936i 0.670503π0.670503\pi
854854 9.83807 0.336652
855855 0 0
856856 −14.3766 −0.491383
857857 −1.71246 −0.0584965 −0.0292483 0.999572i 0.509311π-0.509311\pi
−0.0292483 + 0.999572i 0.509311π0.509311\pi
858858 −5.20094 −0.177557
859859 −22.5749 −0.770246 −0.385123 0.922865i 0.625841π-0.625841\pi
−0.385123 + 0.922865i 0.625841π0.625841\pi
860860 0 0
861861 16.0320 0.546369
862862 10.2459 0.348978
863863 −54.2578 −1.84696 −0.923479 0.383650i 0.874667π-0.874667\pi
−0.923479 + 0.383650i 0.874667π0.874667\pi
864864 −18.5982 −0.632723
865865 0 0
866866 11.8938 0.404169
867867 0 0
868868 −57.2721 −1.94394
869869 −10.8923 −0.369496
870870 0 0
871871 −1.11108 −0.0376474
872872 −14.5995 −0.494400
873873 −20.3677 −0.689343
874874 −1.96030 −0.0663082
875875 0 0
876876 6.96343 0.235273
877877 −14.8989 −0.503099 −0.251549 0.967844i 0.580940π-0.580940\pi
−0.251549 + 0.967844i 0.580940π0.580940\pi
878878 −0.206794 −0.00697896
879879 18.2256 0.614736
880880 0 0
881881 −22.3330 −0.752419 −0.376209 0.926535i 0.622773π-0.622773\pi
−0.376209 + 0.926535i 0.622773π0.622773\pi
882882 −3.25872 −0.109727
883883 −25.3319 −0.852485 −0.426242 0.904609i 0.640163π-0.640163\pi
−0.426242 + 0.904609i 0.640163π0.640163\pi
884884 0 0
885885 0 0
886886 8.57628 0.288126
887887 6.35813 0.213485 0.106743 0.994287i 0.465958π-0.465958\pi
0.106743 + 0.994287i 0.465958π0.465958\pi
888888 8.45584 0.283759
889889 61.8422 2.07412
890890 0 0
891891 4.33194 0.145125
892892 −1.69181 −0.0566459
893893 −28.3497 −0.948686
894894 −1.66417 −0.0556581
895895 0 0
896896 −31.7025 −1.05911
897897 4.28300 0.143005
898898 5.43679 0.181428
899899 45.9037 1.53097
900900 0 0
901901 0 0
902902 −7.07361 −0.235525
903903 −39.5383 −1.31575
904904 −13.1043 −0.435843
905905 0 0
906906 −1.04449 −0.0347007
907907 −13.0295 −0.432636 −0.216318 0.976323i 0.569405π-0.569405\pi
−0.216318 + 0.976323i 0.569405π0.569405\pi
908908 −24.6048 −0.816539
909909 −6.90660 −0.229078
910910 0 0
911911 −20.7685 −0.688093 −0.344046 0.938953i 0.611798π-0.611798\pi
−0.344046 + 0.938953i 0.611798π0.611798\pi
912912 −16.4777 −0.545630
913913 −95.7328 −3.16829
914914 −4.05530 −0.134137
915915 0 0
916916 5.38916 0.178063
917917 32.0988 1.06000
918918 0 0
919919 −5.10970 −0.168553 −0.0842766 0.996442i 0.526858π-0.526858\pi
−0.0842766 + 0.996442i 0.526858π0.526858\pi
920920 0 0
921921 −3.79193 −0.124948
922922 3.40636 0.112183
923923 3.53358 0.116309
924924 44.2918 1.45709
925925 0 0
926926 −5.36349 −0.176255
927927 7.36794 0.241995
928928 19.2396 0.631571
929929 39.6073 1.29947 0.649737 0.760159i 0.274879π-0.274879\pi
0.649737 + 0.760159i 0.274879π0.274879\pi
930930 0 0
931931 −25.7748 −0.844734
932932 37.9464 1.24298
933933 8.93194 0.292419
934934 −0.0129070 −0.000422330 0
935935 0 0
936936 5.47610 0.178992
937937 −39.5575 −1.29229 −0.646144 0.763215i 0.723620π-0.723620\pi
−0.646144 + 0.763215i 0.723620π0.723620\pi
938938 −0.481195 −0.0157116
939939 7.67169 0.250356
940940 0 0
941941 −53.2283 −1.73519 −0.867597 0.497268i 0.834337π-0.834337\pi
−0.867597 + 0.497268i 0.834337π0.834337\pi
942942 4.87022 0.158680
943943 5.82516 0.189693
944944 −20.4143 −0.664430
945945 0 0
946946 17.4450 0.567187
947947 0.773357 0.0251307 0.0125654 0.999921i 0.496000π-0.496000\pi
0.0125654 + 0.999921i 0.496000π0.496000\pi
948948 −4.05086 −0.131566
949949 −8.44812 −0.274238
950950 0 0
951951 −30.4844 −0.988525
952952 0 0
953953 36.8731 1.19444 0.597218 0.802079i 0.296273π-0.296273\pi
0.597218 + 0.802079i 0.296273π0.296273\pi
954954 0.356564 0.0115442
955955 0 0
956956 −51.9309 −1.67956
957957 −35.4999 −1.14755
958958 11.0321 0.356430
959959 −50.7763 −1.63965
960960 0 0
961961 38.5466 1.24344
962962 −5.00217 −0.161276
963963 −20.5973 −0.663738
964964 6.80327 0.219118
965965 0 0
966966 1.85492 0.0596810
967967 −17.8306 −0.573392 −0.286696 0.958022i 0.592557π-0.592557\pi
−0.286696 + 0.958022i 0.592557π0.592557\pi
968968 −26.7210 −0.858846
969969 0 0
970970 0 0
971971 20.3783 0.653970 0.326985 0.945030i 0.393967π-0.393967\pi
0.326985 + 0.945030i 0.393967π0.393967\pi
972972 −28.7693 −0.922775
973973 −60.5768 −1.94200
974974 7.67476 0.245915
975975 0 0
976976 30.0471 0.961785
977977 8.64587 0.276606 0.138303 0.990390i 0.455835π-0.455835\pi
0.138303 + 0.990390i 0.455835π0.455835\pi
978978 −3.02275 −0.0966569
979979 20.2535 0.647306
980980 0 0
981981 −20.9165 −0.667813
982982 −2.66953 −0.0851882
983983 −61.1615 −1.95075 −0.975374 0.220558i 0.929212π-0.929212\pi
−0.975374 + 0.220558i 0.929212π0.929212\pi
984984 −5.39514 −0.171991
985985 0 0
986986 0 0
987987 26.8256 0.853869
988988 21.1195 0.671902
989989 −14.3661 −0.456815
990990 0 0
991991 −27.0979 −0.860792 −0.430396 0.902640i 0.641626π-0.641626\pi
−0.430396 + 0.902640i 0.641626π0.641626\pi
992992 29.1491 0.925484
993993 22.8768 0.725974
994994 1.53035 0.0485397
995995 0 0
996996 −35.6031 −1.12813
997997 −48.3759 −1.53208 −0.766040 0.642793i 0.777775π-0.777775\pi
−0.766040 + 0.642793i 0.777775π0.777775\pi
998998 2.64105 0.0836009
999999 33.0049 1.04423
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 7225.2.a.bg.1.4 6
5.4 even 2 7225.2.a.ba.1.3 6
17.4 even 4 425.2.d.a.101.3 6
17.13 even 4 425.2.d.a.101.4 yes 6
17.16 even 2 inner 7225.2.a.bg.1.3 6
85.4 even 4 425.2.d.b.101.4 yes 6
85.13 odd 4 425.2.c.c.424.7 12
85.38 odd 4 425.2.c.c.424.8 12
85.47 odd 4 425.2.c.c.424.6 12
85.64 even 4 425.2.d.b.101.3 yes 6
85.72 odd 4 425.2.c.c.424.5 12
85.84 even 2 7225.2.a.ba.1.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
425.2.c.c.424.5 12 85.72 odd 4
425.2.c.c.424.6 12 85.47 odd 4
425.2.c.c.424.7 12 85.13 odd 4
425.2.c.c.424.8 12 85.38 odd 4
425.2.d.a.101.3 6 17.4 even 4
425.2.d.a.101.4 yes 6 17.13 even 4
425.2.d.b.101.3 yes 6 85.64 even 4
425.2.d.b.101.4 yes 6 85.4 even 4
7225.2.a.ba.1.3 6 5.4 even 2
7225.2.a.ba.1.4 6 85.84 even 2
7225.2.a.bg.1.3 6 17.16 even 2 inner
7225.2.a.bg.1.4 6 1.1 even 1 trivial